Question

select the correct answer.
of the 27 players trying out for the school basketball team, 8 are more than 6 feet tall and 7 have good aim. what is the probability that the coach would randomly pick a player over 6 feet tall or a player with a good aim? assume that no players over 6 feet tall have good aim.
a. \\(\frac{7}{18}\\)
b. \\(\frac{6}{18}\\)
c. \\(\frac{7}{9}\\)
d. \\(\frac{5}{9}\\)

Explanation:

Step1: Recall the formula for probability of union of two mutually exclusive events

For two mutually exclusive events \( A \) and \( B \) (where \( A \cap B=\varnothing \)), the probability of \( A \) or \( B \) is \( P(A \cup B)=P(A)+P(B) \). Let \( A \) be the event that a player is over 6 feet tall and \( B \) be the event that a player has good aim. We know \( n(A) = 8 \), \( n(B)=7 \), and the total number of players \( N = 27 \). Since no players over 6 feet tall have good aim, \( A \) and \( B \) are mutually exclusive.

Step2: Calculate \( P(A) \) and \( P(B) \)

\( P(A)=\frac{n(A)}{N}=\frac{8}{27} \), \( P(B)=\frac{n(B)}{N}=\frac{7}{27} \)

Step3: Calculate \( P(A \cup B) \)

Using the formula for mutually exclusive events, \( P(A \cup B)=P(A)+P(B)=\frac{8}{27}+\frac{7}{27}=\frac{8 + 7}{27}=\frac{15}{27}=\frac{5}{9} \)

Answer:

D. \(\frac{5}{9}\)